The language and ideas of dynamical
systems theory that have been developed over the last century have
become ubiquitous in the applied sciences. However, two fundamental
developments are impacting the form and use of quantitative models
of dynamics: the increasing importance in multiscale
problems, and the revolutionary impact of rapidly evolving
information technologies. In particular, while the analytic
language of **differential equations **and **iterations maps** is still
the basis for most quantitative descriptions of scientific ideas,
current results are often obtained directly through data mining or
machine learning applied to experimental data or through numerical
simulations of models which are not derived from first principles and often involve
considerable uncertainty.

It is important to recognize that
the lack of a traditional mathematical model is not a sign of
resistance to mathematics, but often an indication of the enormity
and complexity of the problem and of the fact that there is no closed-form
mathematical formulation that captures all the relevant information. In summary
the scientific community is attempting to deal with problems, such
as for example climate change, gene regulatory/signal transduction networks,
neuroscience, ecology, etc., for which the nonlinearities are
often derived based on heuristic principles or tremendous simplifications,
the associated parameters are poorly measured or even unknown, the experimental
measurements are not necessarily accurate nor complete, and yet
there may be vast amounts of data.

In this workshop we will bring together
a small group of researchers to collaborate on the problems sketched above.